L_p Quantile Regression With Realized Measure

We combine Lp quantile regression with realized measure and call it realized Lp quantile regression(Realized Lp),through incorporating measurement equation into the conventional Lp quantile regression model,in a framework analogous to Realized-GARCH.We use Realized Variance(RV)and Realized Range(RR)with different inter-vals as the employed realized measures.These are modeled in the measurement equa-tion.We find exponential power distribution allows likelihood to be developed,that facilitates pseudo-maximum likelihood estimation.We have a simulation to ascertain whether the model can estimate parameters correctly.Afterwards,we analyze empiri-cal results by using S&P 500.Both the parameters estimated and returns forecasted are analyzed.Furthermore,we also compare RV and RR with different intervals to find out which realized measures are the best.Finally,we'll compare different p in Lp quantile regression.Then more indices are used,and we find that L1.2 suits for most indices.